| Line 8: | Line 8: | ||
<br> | <br> | ||
<math>A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)</math> | <math>A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right)</math> | ||
| − | <math>A | + | <br> |
| + | <math>A^-1\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right)</math> | ||
<h3> Theorem 1 </h3> | <h3> Theorem 1 </h3> | ||
Revision as of 06:54, 10 December 2012
Inverse of a Matrix
An n x n matrix A is said to have an inverse provided there exists an n x n matrix B such that AB = BA = In. We call B the inverse of A and denote it as A-1. Thus, AA-1 = A-1A = In. In this case, A is also called nonsingular.
Example.
$ A = \left(\begin{array}{cccc}4&3\\3&2\end{array}\right) $
$ A^-1\left(\begin{array}{cccc}-2&3\\3&-4\end{array}\right) $
Theorem 1
The inverse of a matrix, if it exists, is unique
Theorem 2
If A and B are both nonsingular n x n matrices (i.e. invertible), then AB is nonsingular and (AB)-1 = B-1A-1.
